It looks like you've uploaded a worksheet titled
"Solving Rational Equations 1" with several rational equations to solve. Since I can't view images directly, I’ll need you to provide the actual equations from the image (or type them out), so I can help you solve and explain each one.
However, based on the structure of such worksheets, here’s what typically appears:
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General Instructions for Solving Rational Equations:
1.
Identify restrictions: Determine values that make any denominator zero (these are excluded from the solution).
2.
Multiply both sides by the LCD (Least Common Denominator) to eliminate denominators.
3.
Solve the resulting equation (usually linear or quadratic).
4.
Check for extraneous solutions by plugging back into the original equation (especially important in rational equations).
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Example Problem (if it were visible):
Suppose one of the problems is:
$$
\frac{2}{x} + \frac{1}{x+1} = \frac{3}{x(x+1)}
$$
#### Step-by-step Solution:
1.
Restrictions: $ x \neq 0 $, $ x \neq -1 $
2.
LCD: $ x(x+1) $
3. Multiply both sides:
$$
x(x+1)\left(\frac{2}{x} + \frac{1}{x+1}\right) = x(x+1)\left(\frac{3}{x(x+1)}\right)
$$
$$
2(x+1) + x = 3
$$
$$
2x + 2 + x = 3
\Rightarrow 3x + 2 = 3
\Rightarrow 3x = 1
\Rightarrow x = \frac{1}{3}
$$
4.
Check: $ x = \frac{1}{3} $ is not restricted → valid.
✔ Final Answer: $ \boxed{\frac{1}{3}} $
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Now, please
type out the equations from your worksheet, and I’ll solve each one step-by-step with explanations!
Parent Tip: Review the logic above to help your child master the concept of rational equation worksheet.
